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arXiv · 2301.13579

Twisted cohomology and likelihood ideals

Saiei-Jaeyeong Matsubara-Heo·Simon Telen
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Abstract

A likelihood function on a smooth very affine variety gives rise to a twisted de Rham complex. We show how its top cohomology vector space degenerates to the coordinate ring of the critical points defined by the likelihood equations. We obtain a basis for cohomology from a basis of this coordinate ring. We investigate the dual picture, where twisted cycles correspond to critical points. We show how to expand a twisted cocycle in terms of a basis, and apply our methods to Feynman integrals from physics.

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Saiei-Jaeyeong Matsubara-Heo, Simon Telen. 2023-01-31. Twisted cohomology and likelihood ideals. https://arxiv.org/abs/2301.13579

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